Integral calculator with steps

ืžื›ื™ืœ ืžื•ื“ืขื•ืช
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ื”ื•ืจื“ื•ืช
ืกื™ื•ื•ื’ ืชื•ื›ืŸ
ื›ื•ืœื
ืฆื™ืœื•ื ืžืกืš
ืฆื™ืœื•ื ืžืกืš
ืฆื™ืœื•ื ืžืกืš
ืฆื™ืœื•ื ืžืกืš
ืฆื™ืœื•ื ืžืกืš
ืฆื™ืœื•ื ืžืกืš
ืฆื™ืœื•ื ืžืกืš

ืžื™ื“ืข ืขืœ ื”ืืคืœื™ืงืฆื™ื” ื”ื–ื•

ืžื—ืฉื‘ื•ืŸ ืื™ื ื˜ื’ืจืœื™ ื–ื” ื›ืืŸ ื›ื“ื™ ืœืขื–ื•ืจ ืœืš ืœืคืชื•ืจ ืืช ื—ื™ืฉื•ื‘ื™ ื”ืื™ื ื˜ื’ืจืฆื™ื” ืฉืœืš ืชื•ืš ื–ืžืŸ ืงืฆืจ. ื›ื™ื“ื•ืข ืฉื™ืฉื ื” ืชืžื™ื“ ืคืขื•ืœื” ื”ืคื•ื›ื”, ืœื›ืœ ื”ืคืขื•ืœื•ืช ื›ื’ื•ืŸ ืกื™ื›ื•ื ื•ื—ื™ืกื•ืจ, ื›ืคืœ ื•ื—ืœื•ืงื” ื‘ืžืชืžื˜ื™ืงื”. ื•ืชื”ืœื™ืš ื”ืคื•ืš ื–ื” ื™ื“ื•ืข ื›ืื ื˜ื™-ื‘ื™ื“ื•ืœ ืื• ืื™ื ื˜ื’ืจืฆื™ื” ืคืฉื•ื˜ื” ืœืชื”ืœื™ืš ื”ื”ื‘ื—ื ื”.

ืื™ื ื˜ื’ืจืœ ื”ื•ื ืคื•ื ืงืฆื™ื” ื ืชื•ื ื” ื‘ื ื’ื–ืจืช ืฉื›ืืฉืจ ืื ื• ืžื‘ื“ื™ืœื™ื ืื•ืชื” ื•ืื•ืžื“ื™ื ืืช ื”ืฉื˜ื— ืžืชื—ืช ืœืขื™ืงื•ืœ ื’ืจืฃ ื”ืคื•ื ืงืฆื™ื”, ืงื•ื‘ืขืช ืืช ื”ืคื•ื ืงืฆื™ื” ื”ื ืชื•ื ื”.

ื›ื“ื™ ืœื—ืฉื‘ ืืช ื”ืฉื“ื”, ื”ืื•ืจืš, ื ืงื•ื“ื•ืช ื”ืžืจื›ื– ื•ืคืจื™ื˜ื™ื ืฉื™ืžื•ืฉื™ื™ื ืจื‘ื™ื ืื—ืจื™ื, ื ื™ืชืŸ ืœื”ืฉืชืžืฉ ื‘ืื™ื ื˜ื’ืจืฆื™ื”. ื‘ืืคืฉืจื•ืชืš ืœืคืชื•ืจ ืืช ื”ืื™ื ื˜ื’ืจืฆื™ื” ื‘ืงืœื•ืช ื‘ืืžืฆืขื•ืช ืžื—ืฉื‘ื•ืŸ ื—ื™ื ืžื™ ื–ื”, ืืš ื”ื—ืœ ืžื”ืคื•ื ืงืฆื™ื” ืœืžืฆื•ื ืืช ื”ืฉื˜ื— ืฉืžืชื—ืช ืœืขืงื•ืžื” ื”ื™ื ื”ื“ืจืš ื”ืคืฉื•ื˜ื” ื•ื”ืžื”ื™ืจื” ื‘ื™ื•ืชืจ ืœืคืชื•ืจ ืืช ื”ืื™ื ื˜ื’ืจืฆื™ื”.
ืกื•ื’ื™ ืื™ื ื˜ื’ืจืœื™ื

ื™ืฉื ื ืžื’ื•ื•ืŸ ืกื•ื’ื™ ืื™ื ื˜ื’ืจืœื™ื, ืืš ืกื•ื’ื™ ื”ืื™ื ื˜ื’ืจืœื™ื ื”ื ืคื•ืฆื™ื ื‘ื™ื•ืชืจ ื”ื:

ืื™ื ื˜ื’ืจืœื™ื ืžื•ื’ื“ืจื™ื
ืื™ื ื˜ื’ืจืœื™ื ื‘ืœืชื™ ืžื•ื’ื“ืจื™ื

ืžื—ืฉื‘ื•ืŸ ืื™ื ื˜ื’ืจืฆื™ื” ืžืงื•ื•ืŸ ื–ื” ื™ืขื–ื•ืจ ืœืš ืœืžืฆื•ื ืืช ืฉื ื™ื”ื, ืœื ืžืฉื ื” ืขื ืื™ื–ื” ืกื•ื’ ืืชื” ืขื•ื‘ื“.
ื›ื™ืฆื“ ืœื”ืฉืชืžืฉ ื‘ืžื—ืฉื‘ื•ืŸ ื–ื” ืœื”ืขืจื›ื” ืื™ื ื˜ื’ืจืœื™ืช?
ืžื—ืฉื‘ื•ืŸ ืื™ื ื˜ื’ืจืœื™ ื–ื” ื”ื•ื ื™ื™ืฉื•ื ืžืงื•ื•ืŸ ื‘ื—ื™ื ื ืฉื™ื›ื•ืœ ืœื”ืžื—ื™ืฉ ืืช ื”ื—ืฉื™ื‘ื•ืช ืฉืœ ืื™ื ื˜ื’ืจืœื™ื ืžื•ื’ื“ืจื™ื ืื• ืื™ื ื˜ื’ืจืœื™ื ืื™ื ืกื•ืคื™ื™ื ืฉืœ ื›ืœ ื”ืคื•ื ืงืฆื™ื•ืช ื”ืื™ื ื˜ื’ืจืœื™ื•ืช. ืžื›ื™ื•ื•ืŸ ืฉื”ื•ื ืžืจืื” ืืช ื”ืชื•ืฆืื•ืช ื‘ืฉื‘ืจื™ืจ ืฉื ื™ื•ืช, ื–ื•ื”ื™ ื“ืจืš ืคืฉื•ื˜ื” ื™ื•ืชืจ ืœืžื“ื•ื“ ืžืกืคืจื™ื ืฉืœืžื™ื.

ื”ื–ืŸ ืจืง ืืช ืกื•ื’ ื”ืื™ื ื˜ื’ืจืœ ืฉื‘ืจืฆื•ื ืš ืœื”ื•ืกื™ืฃ ืœืื—ืจ ื”ืชืงื ืช ืืคืœื™ืงืฆื™ื” ื–ื• ืžื—ื ื•ืช ื”ืคืœื™ื™ ื‘ืกืžืืจื˜ืคื•ืŸ ืฉืœืš.

ื”ืžื—ืฉื‘ื•ืŸ ื™ื™ืฆื’ ืืช ื‘ื™ื˜ื•ื™ ื”ืงืœื˜ ืฉืœืš ื‘ืฆื•ืจื” ื’ืจืคื™ืช, ื•ืื– ืœื—ืฅ ืขืœ ื›ืคืชื•ืจ ื”'ื—ืฉื‘ 'ืื ื–ื” ื‘ื“ื™ื•ืง ื›ืžื• ืฉืืชื” ืจื•ืฆื”.

ื”ืžืกืš ืฉืœืš ื™ื‘ื™ื ืืช ื”ืชื•ืฆืื•ืช ืชื•ืš ืฉื ื™ื•ืช.

ื‘ืขื•ื“ ืฉืžื—ืฉื‘ื•ื ื™ื ืื™ื ื˜ื’ืจืœื™ื™ื ืขื•ื–ืจื™ื ืœืชืคืงื•ื“ื™ื ืžื•ื’ื“ืจื™ื ื•ืœื ืžื•ื’ื“ืจื™ื ืฉืœ ืžืกืคืจ ืžืฉืชื ื™ื, ืชื—ื™ืœื” ืขืœื™ืš ืœื™ื™ืฉื ื’ื‘ื•ืœื•ืช ื‘ืžืงืจื” ืฉืœ ืคืชืจื•ืŸ ืื™ื ื˜ื’ืจืœื™ื ืžื•ื’ื“ืจื™ื.

ื‘ืกื•ืคื• ืฉืœ ื“ื‘ืจ ื–ื• ืฉื™ื˜ื” ืฆืขื“ ืื—ืจ ืฆืขื“ ืœืคืชื•ืจ ื•ืœืชืคื•ืก ืื™ื ื˜ื’ืจืœื™ื, ืืš ืคื•ืชืจ ื–ื” ืžืืคืฉืจ ืœื ื• ืœืจื•ืฅ ืžืจื—ื•ืง ืžื›ื™ื•ื•ืŸ ืฉื”ื•ื ืžืืžืฅ ืืช ื›ืœ ืฉื™ื˜ื•ืช ื”ืื™ื ื˜ื’ืจืฆื™ื” ื•ืืคื™ืœื• ืคื•ื ืงืฆื™ื•ืช ืžื™ื•ื—ื“ื•ืช ื‘ื›ื“ื™ ืœืกืคืง ืคืชืจื•ื ื•ืช ื›ืœืœื™ื™ื.
ืžื“ื•ืข ืœื”ืฉืชืžืฉ ื‘ืžื—ืฉื‘ื•ืŸ ื–ื” ื›ื“ื™ ืœืคืชื•ืจ ื‘ืขื™ื™ืช ืื™ื ื˜ื’ืจืฆื™ื”?

ื”ื”ืกื‘ืจื™ื ืžื“ื•ืข ืขืœื™ื›ื ืœื”ืฉืชืžืฉ ื‘ืžื—ืฉื‘ื•ืŸ ืื™ื ื˜ื’ืจืœื™ ื–ื” ื›ื“ื™ ืœืคืชื•ืจ ืคื•ื ืงืฆื™ื•ืช ืื™ื ื˜ื’ืจืฆื™ื” ืžื•ืฆื’ื™ื ืœื”ืœืŸ.

ืžื—ืฉื‘ื•ืŸ ืื™ื ื˜ื’ืจืœื™ ื–ื” ื”ื•ื ืืคืœื™ืงืฆื™ื” ืžืงื•ื•ื ืช ื‘ื—ื™ื ื ื”ืžืืคืฉืจืช ืœืš ืœื—ืฉื‘ ืืช ื”ืื™ื ื˜ื’ืจืœ ื‘ืื•ืคืŸ ืžืงื•ื•ืŸ ืžืื•ื“ ื•ืขื•ื–ืจืช ืœืื™ืžื•ืช ืขื ืžืกืคืจ ืžืฉืชื ื™ื ืฉืœ
ืฉื™ืœื•ื‘ ืคื•ื ืงืฆื™ื•ืช.

ื–ื” ื™ืžื ืข ืžืžืš ืœื‘ืฆืข ืืช ื”ื—ื™ืฉื•ื‘ื™ื ื‘ืื•ืคืŸ ื™ื“ื ื™ ื›ื“ื™ ืœื”ื‘ื™ืŸ ืืช ืžื˜ืจืชื ืฉืœ ืื™ื ื˜ื’ืจืœื™ื ืžืกื•ื™ืžื™ื ื•ืชื•ื›ืœ ืœื”ืฉื™ื’ ืืช ื”ืชื•ืฆืื•ืช ื‘ืขื–ืจืช ืฉื™ืžื•ืฉ ื‘ืžื—ืฉื‘ื•ืŸ ืื™ื ื˜ื’ืจืœื™ ืžืงื•ื•ืŸ.

ืœื ืจืง ืฉืžื—ืฉื‘ื•ืŸ ืื™ื ื˜ื’ืจืœื™ ื–ื” ืžืกื™ื™ืข ื‘ื–ื™ื”ื•ื™ ื”ื“ืจืš ื”ื”ืคื•ื›ื” ืœื ื˜ื™ืœืช ื”ื ื’ื–ืจืช, ืืœื ื”ื•ื ื’ื ืขื•ื–ืจ ืœืืชืจ ื‘ืขื™ื•ืช ื‘ืฉื˜ื—.


ืคืชืจื•ืŸ ืคื•ื ืงืฆื™ื•ืช ืื™ื ื˜ื’ืจืฆื™ื” ื™ื›ื•ืœ ืœื”ื™ื•ืช ืขื‘ื•ื“ื” ืงื“ื—ืชื ื™ืช ืžืื•ื“ ืขื‘ื•ืจ ืื•ืชื ืกื˜ื•ื“ื ื˜ื™ื ืขื ืจืงืข ืœื ื˜ื›ื ื™. ืฉื™ืจื•ืชื™ ื™ื™ืฉื•ื ื–ื” ืขื•ื–ืจื™ื ืœืš ืœื”ืชื’ื‘ืจ ื‘ืžื”ื™ืจื•ืช ื•ื‘ื™ืขื™ืœื•ืช ืขืœ ืืชื’ืจื™ื ืืœื”.

ืžื—ืฉื‘ื•ืŸ ื–ื” ื’ื ื™ื•ืขื™ืœ ืœื›ื ื›ืืฉืจ ื ืื‘ืงื™ื ื‘ืžืฉื•ื•ืื•ืช ืื™ื ื˜ื’ืจืฆื™ื” ืžื•ืจื›ื‘ื•ืช ื‘ื—ืฉื‘ื•ืŸ ื•ื‘ืžืชืžื˜ื™ืงื” ืžื›ื™ื•ื•ืŸ ืฉื™ืฉ ืœื• ืฉื™ื˜ื•ืช ืื™ื ื˜ื’ืจืฆื™ื” ืกื˜ื ื“ืจื˜ื™ื•ืช ื›ืžื• ื’ื ืชื›ื•ื ื•ืช ืื™ื ื˜ื’ืจืฆื™ื” ืžื™ื•ื—ื“ื•ืช.


ืื ืืชื” ืžื ืกื” ืœืืชืจ ืืช ื”ืื™ื ื˜ื’ืจืœื™ื, ืืชื” ื™ื›ื•ืœ ืœื”ืฉืชืžืฉ ื‘ืžื—ืฉื‘ื•ืŸ ื–ื” ื›ื“ื™ ืœื—ืคืฉ ืืช ื”ืชื’ื•ื‘ื•ืช. ืœื›ืŸ, ื›ืฉืขื•ืฉื™ื ืฉื™ืขื•ืจื™ ื‘ื™ืช ื•ืžืฉื™ืžื•ืช, ื–ื” ื’ื ื™ืขื•ื“ื“ ืืชื›ื ืœื‘ื“ื•ืง ืฉื•ื‘ ืืช ื”ืชื’ื•ื‘ื•ืช ืฉืœื›ื.
ืชื›ื•ื ื•ืช ืฉืœ ืืคืœื™ืงืฆื™ื” ื–ื• - ืžื—ืฉื‘ื•ืŸ ืื™ื ื˜ื’ืจืœื™ ืื• ืืคืœื™ืงืฆื™ื™ืช ืื™ืชื•ืจ ืื™ื ื˜ื’ืจืฆื™ื”:
ืœืชืช ืชื•ืฆืื•ืช ืžื™ื™ื“ื™ื•ืช
100% ื‘ื˜ื•ื— ื•ืžืื•ื‘ื˜ื— ืœืฉื™ืžื•ืฉ
ื—ื•ืกืš ืœืš ื–ืžืŸ
ืœืœื ืขืœื•ืช ืœื—ืœื•ื˜ื™ืŸ
ืžืืชืจ ืื™ื ื˜ื’ืจืฆื™ื” ื‘ื–ืžืŸ ืืžืช ื‘ื—ื ื•ืช ื”ืคืœื™ื™
ืœืกืคืง ืชื•ืฆืื•ืช ืจืง ืขืœ ื™ื“ื™ ื”ื–ื ืช ื‘ื™ื˜ื•ื™ ื”ืื™ื ื˜ื’ืจืฆื™ื”
ืื ืืชื” ื ืชืงืœ ื‘ื‘ืขื™ื” ื›ืœืฉื”ื™ ื‘ืขืช ื”ื•ืจื“ืช ืื• ืฉื™ืžื•ืฉ ื‘ืืคืœื™ืงืฆื™ื™ืช ื”ืžื—ืฉื‘ื•ืŸ ืฉืœื ื•, ืื ื ื™ื™ื“ืข ืื•ืชื ื• ืขืœ ืžื ืช ืฉื ื•ื›ืœ ืœืชืงืŸ ืื•ืชื”.
ืขื“ื›ื•ืŸ ืื—ืจื•ืŸ ื‘ืชืืจื™ืš
12 ื‘ืกืคื˜ืณ 2025

ืื‘ื˜ื—ืช ื ืชื•ื ื™ื

ื›ื“ื™ ืœืฉืžื•ืจ ืขืœ ื”ื‘ื˜ื™ื—ื•ืช ืฆืจื™ืš ืงื•ื“ื ื›ืœ ืœื”ื‘ื™ืŸ ืื™ืš ื”ืžืคืชื—ื™ื ืื•ืกืคื™ื ื•ืžืฉืชืคื™ื ืืช ื”ื ืชื•ื ื™ื ืฉืœืš. ื ื•ื”ืœื™ ืคืจื˜ื™ื•ืช ื”ื ืชื•ื ื™ื ื•ืื‘ื˜ื—ืช ื”ื ืชื•ื ื™ื ืขืฉื•ื™ื™ื ืœื”ืฉืชื ื•ืช ื‘ื”ืชืื ืœืฉื™ืžื•ืฉ, ืœืื–ื•ืจ ื•ืœื’ื™ืœ ื”ืžืฉืชืžืฉ. ื”ืžืคืชื— ืกื™ืคืง ืืช ื”ืžื™ื“ืข ื”ื–ื” ื•ื”ื•ื ืขืฉื•ื™ ืœืขื“ื›ืŸ ืื•ืชื• ืžื“ื™ ืคืขื.
ื”ืืคืœื™ืงืฆื™ื” ื”ื–ืืช ืขืฉื•ื™ื” ืœืฉืชืฃ ืืช ืกื•ื’ื™ ื”ื ืชื•ื ื™ื ื”ืืœื” ืขื ืฆื“ื“ื™ื ืฉืœื™ืฉื™ื™ื
ืžื–ื”ื” ื”ืžื›ืฉื™ืจ ืื• ืžื–ื”ื™ื ืื—ืจื™ื
ื”ื ืชื•ื ื™ื ืžื•ืฆืคื ื™ื ื‘ื–ืžืŸ ื”ื”ืขื‘ืจื”
ืื™ ืืคืฉืจ ืœืžื—ื•ืง ืืช ื”ื ืชื•ื ื™ื